Abstract
In a recent paper (Olver 1954) I considered asymptotic expansions of solutions of the differential equation dz2 {up(z)+q(z)}w, ( M ) for large positive values of the parameter
u
, which are uniform with respect to
z
when
z
lies in a simply-connected domain D in which
p(z)
,
q(z)
are analytic functions of
z
independent of
u
.Three cases A, B and C were considered. In case A the equation had no transition points in D. In case B there was one transition point in D, a simple zero of
p(z)
. In case C there was again one transition point, this time a double pole of
p(z)
. It was shown that case C can be transformed into case A.
Reference4 articles.
1. Erdelyi A. 1955 Asymptotic expansions. Tech. Rep. no. 3 California Institute of Technology.
2. Watson G. N. 1944 Theory of Besselfunctions. Cambridge University Press. IN T R O D U C IN G A V O LU M E S U B S C R IP T IO N RATE
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